Closely related to 2-RIT is the square root sum problem problem where the goal is to infer the sign of a given linear combination of square roots. This is a notorious open problem in numerical analysis and computational geometry. It is known to be decidable in the Counting Hierarchy and the question of determining its precise computational complexity remains open since it was explicitly posed by Garey, Graham and Johnson [1]} in 1976. Along with the related problem of determining the sign of an integer computed by a variable-free algebraic circuit, the square root sum problem is frequently used as a tool for proving hardness and obtaining upper bounds in quantitative verification [2]}, [3]}, [4]}, [5]}, algorithmic game theory [6]}, [7]}, [8]}, formal language theory and logic [9]}, [10]}. We refer the interested reader to [11]}, [12]} and the references therein for a discussion on the complexity status of the square root sum problem and related geometric questions.
